A CHAOTIC SYSTEMS ANALYSIS OF THE NASAL CYCLE

by Michael Winkler, Allan Combs, and Colin Daley

University of North Carolina at Asheville

The nasal cycle is a chaotic ultradian rhythm with a period ranging &om about 75 to 200 minutes. It has been shown to correlate highly with EEG amplitude in the contralateral hemisphere at virtually all frequencies, suggesting a connection between this rhythm and laterality of brain bc t ion . During a three-week period, five participants estimated airflow from both nostrils every 30 minutes during waking hours. Estimates were recorded on Likert scales and analyzed in three distinct phases: (1) reconstructing two- dimensional attractors by lagging and embeddins (2) computing Fourier frequency analyses; and (3) estimating fractal dimensions. Attractor reconstructions demonstrate noticeable order when compared to Monte Car10 reconstructions of the same data sets, and dimension estimates are in the fractal range. The attractor reconstructions, in combination with the frequency analyses, show distinct individual differences in the structure of the nasal cycle. The advantages of cbaotic s y s t e m analyses over traditional behavioral statistics are discussed.

KEY WORDS: chaos, chaotic systems, nonlinear dynamics, ultradian rhythms, nasal cycle TYPE OF ARTICLE: chaos theory application DIMENSIONS AND UNITS: Likert scale

NASAL RHYTHMS

HE NASAL CYCLE IS AN ultradian rhythm in which a predominance T of air flows alternately through

one nostri l then the other. I t i s produced by a dynamic alteration of the blood flow t o the nasal mucosa, causing al ternat ive swelling and shrinking of tissue (Funk, 1980; Rossi, 1986). Werntz, Bickford, Bloom, and Shannahoff (1981) suggest t h a t the cycle i s p a r t of a larger rhythm in sympathetic and parasympathetic lateral dominance throughout the body. Studies report a wide range of nostril

cycle durations, from roughly 1.25 to 4.3 hours (Clark, 1980; Funk, 1980). Werntz e t a1.(1981) found t h a t t he changing dominance i s strongly correlated with the EEG amplitude of the contralateral cerebral hemisphere at virtually all frequencies. They further found that the dominant airflow as well as the correlated EEG component could be shifted in about half-a-minute by forcibly brea th ing through the nondominant nostril, e.g., by placing a cotton ball in the dominant one.

Funk (1980) speculated that the nasal cycle is a subsystem of the Basic Rest Activity Cycle. Both are apparently

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regulated by the autonomic nervous system, and display roughly similar periodicities t o certain of the latter's other components, such as body activity (Clements e t al., 19761, hear t ra te (Anch et al., 1976; Broughton & Baron, 1978; Friedell, 1948; Lovett, 1980; Wilson et al., 19771, respiration (Home & Whitehead, 1976), and body temperature (Hunsaker et al., 1977; Wilkenson, 1982).

Interestingly, voluntary control of nostril dominance has been par t of certain yogic traditions since ancient times. These associate right nostril dominance with an active psychological state and left dominance with a passive one (Ballentine, 1980; Funk, Clarke, 1980; Rossi, 1986). Modem studies may validate or further clarify the meaning of such ancient ideas. The work of Eccles (19781, Funk and Clark (19801, Ballentine (19801, and Wertz e t al. (1981) give preliminary evidence supporting a partial psychophysiological basis for the nasal cycle. These studies show positive correlations between cerebral hemispheric activity and the ultradian rhythm of the nasal cycle. Due t o its connection to physiological processes i t has been deemed the "windown of the autonomic nervous system (Rossi, 1986).

CHA(yT1C SYSTEMS ANALYSIS An overview of the current literature

on the nasal cycle reveals one central theme, namely that the periodicity of the cycle is irregular. Results obtained by Funk and Clarke (1980) and by Ballentine (1980) show large variability, both between and within individuals even during the course of a single day, though a rough cyclicity is apparent in the longer averages. Clarke (1980) and Dallimore and Eccles (1977) suggest that this high degree of variability is in par t due t o a high sensitivity t o a multitude of both internal and external influences. Whatever the reasons, i t i s apparent t ha t th i s

ultradian rhythm is both cyclic and highly irregular.

Although early applications of chaotic systems theory were restricted at first to the physical sciences, recent attention has also been given to the biological and social sciences (Abraham, 1991; Harth, 1983; Levine & Fitzgerald 1992; Loye & Eider, 1987. It is becoming apparent that many phenomena in all these fields consist of chaotic regimes (Crutchfield, Doyne, Packard, & Shaw, 1986). In such regimes relatively simple systems driven by a few variables can exhibit highly complex chaotic behavior which, in turn, may be described by relatively simple dynamical laws (Basar, 1991; Rapp, Bashore, Martinerie, Albano, Mees, 1989).

Previous studies of the nasal cycle have been constrained by analyses based on traditional linear statistical models. Although these provided valuable information, they failed to account for the irregularities of the nostril rhythm other than in terms of error variance. The present study describes the nasal cycle from a non-linear chaotic systems perspective. This approach t rea ts previously unaccountable variance a s integral to the complex structure of the chaotic process itself.

METHOD

SUBJECTS Five undergraduate students, all

male, participated. Their ages ranged from roughly 20 to 50 years.

MATERIALS AND PROCEDURE Likert scales were used by each

participant to record nostril dominance every waking 30 minutes during a three- week period. Breath flowing solely in the left nostril was marked at the left end of the scale. Breath flowing solely in the right nostril was marked at the right, and equal flow through both nostrils was marked at the center. The scales were presented as straight lines 4

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NASAL CYCLE 287

cm in length. Each was marked with a slash to indicate nostril dominance. For this, participants received booklets in which each of 21 pages, 1 per day, contained sufficient Likert scales for a new one t o be marked each thir ty minutes throughout the waking day. Participants carried the books with them, finding that with a little practice they had no difficulty remembering to mark them (Hanna, 1991).

The participants learned to estimate t h e re la t ive airflow through each nostril by pressing lightly on each side of the nose, compressing i t s nostril, and judging the ease of flow through the opposite side. Pilot studies in our laboratory have confirmed t h e reliability of this technique, and our results appear consistent with those of previous s tudies (Heetderks, 1927; Eccles, 1978; Clarke, 1980; Funk & Clark, 1980).

ANALYSES AND DISCUSSION

ATTRACTOR RECONSTRUCTIONS Attractor reconstructions were made

for each participant by interpolating four points between each successive pair of Likert values and performing a three point running average on the result. The subsequent data sets were lagged three units against themselves ( t h e equiva len t t o . 3 hour ) a n d reconstructed as attractors (Figure 1). These reconstructions were done on a personal computer using Schaffer’s Dynamical Software (1988).

The reconstructions have a similar appearance t o s t r ange (chaotic) a t t r ac to r s . To a s su re ourselves t h a t t h i s appearance i s not due t o chance alone we performed several reconstruct ions from d a t a se t s for which we randomized the order of the Likert values (Hanna, 1991). This Monte Carlo procedure yielded attractor-like reconstructions of dis- tinctly different appearance (Figure l), especially when viewed in real time.

FRACTAL DIMENSION Fur the r evidence t h a t t h e reco-

nstructions are not random, but exhibit aspects of a chaotic-like process, was obtained from computations of the fractal dimension. These were performed using Sarraille and DiFalco’s (1992) fractal dimension program for the personal computer.

The subsequent values (Table 2) were surprisingly s imilar for a l l participants, ranging from 1.67 to 1.79 for t he information dimension, and from 1.66 t o 1.81 for the correlation dimension. These values suggest fractal- like complexity

FREQUENCY SPECTRA An alternative procedure for viewing

cyclic processes is the spectral analysis. Using Schaffer’s Dynamical Software, such an analysis was performed on each participant’s record.

The resul t ing power spectra a r e shown in Figure 3. The most interesting feature of these spectra is that certain of them, such as those for participants 2 and 5, exhibit dominant frequency peaks, or regions, while others, such as those for participants 1 and 3, display none at all. As shown by the attractor reconstructions, however, all arise from non-random temporal processes.

m M D U A L DIFFERENCES The present procedure disclosed

consistent and notable differences between t h e pa t t e rns of individual participants. These differences are seen both in the attractor reconstructions and in the power spectra.

The power spectrum for participant 2 shows a peak periodicity at roughly 4 hours and a smaller one a t a bit less than 3 hours. These periodicities are in l ine with those reported in several previous studies (e.g., Werntz, Bickford, Bloom, Shannahoff 1981; Clarke, 1980; Keuning, 1963; Eccles, 1978). On the other hand, par t ic ipant 5 shows no single definitive peak, but a strong

Behavioral Science, Vdume 39,1(394

sub 1

aub 4 0

L

B u b 5 I-

lub $ -Random

FIGURE 1

Two-dimensional attractor reconstructions of the nasal cycle. Responses of sub 5 were randomized and reconstructed using the same proceedure. Maximum and minimum values are:

S1: 5-35; S2: 9-37; S3: 17-24; S4: 4-36; S5: 9-40; Random: 9-40.

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NASAL CYCLE 289

Information I Correlation

1.70711

1.68238

1.69535

1.67119

1.77199

1.81131

1.78483

1.66078

1.66264

TABLE 1

Fractal Dimension Estimates

component in the general neighborhood of 8 hours. Since records were kept only during the roughly 16 hours of wakefulness, this peaked region represents two cycles per day.

The attractor reconstructions reveal other characteristics. Participants 4 and 5 exhibit roughly symmetrical attractors, indicating that about equal time is spent with the left and right nostrils dominant. Moreover, the open space in the center of each indicates tha t neither participant spent as much time in an equal or balanced state as with one or the other of the nostrils dominant. The long outer trajectories of participant 5’s recon- struction are suggestive of the strong, smooth cycles seen in his power spectrum. On the other hand, participants 1 and especially 2 exhibit an asymmetry towards the upper right, indicating a dominance of the right nostril in these individuals.

The size of each attractor is an indication of the extent to which its rhythm swings to strongly lateralized extremes or tends, alternatively, to stay near the center

where air flow is equal between the nostrils. Participant 5, for instance, swings widely, between scale locations of 9 and 40, while participant 3 varies only between 17 and 24.

THE ADVANTAGES OF CHAOTIC SYSTEMS ANALYSIS

The nostril rhythm exhibits a remarkable degree of variability between and within individuals. Attributing such variability simply to error variance seems unproductive and pointless. Such chaotic phenomena are far from unknown in the biological and behavioral sciences. They are ideally modeled by chaotic systems analyses which treat their unpredictable and seemingly erratic behavior as part of an exquisite chaotic structure. Chaotic processes have been shown mathe- matically to be potentially comprised of surprisingly few actual variables interacting in a nonlinear fashion (e.g., Crutchfield, et al. 1986). Thus, there is hope that the seemingly erratic nostril rhythm may one day succumb to a relatively simple evaluation.

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sub 1

7

houn

u b 2 i t i a 4 2

haun

FIGURE 2

Fourier frequency analysis presented as periodicity (1 I f ) between 2 and 32 hours. 16 hours is roughly circadian, as subjects averaged about 8 hours of sleep in a 24 hour day.

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NASAL CYCLE 29 1

Here we emphasize the descriptive potential offered by chaos analyses for characterizing phenomena heretofore understood predominantly in terms of error or noise. Previous investigations of the nostril cycle failed, for the most part, to represent its irregular oscillations other than in the roughest terms, while the present approach reveals the complexities and nuances of this rhythm. In doing so, it shifts the stress away from the dominant nomothetic mode, which emphasizes group data, back to the idiographic mode, which emphasizes individual differences, once a more favored approach in behavioral and psychological analysis than in recent years.

The question of whether systems such as t h e nostril rhythm are truly chaotic, producing mathematically pure strange attractors, is less important than the fact that the chaotic systems approach is a fresh and potentially powerful methodology available to a significant realm of phenomena previously intractable to linear methods. In doing so, it shifts to an idiographic and process oriented perspective on behavior.

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